The recent atmospheric neutrino data from Super-Kamiokande
(Fukuda et al. 1998)
provide strong evidence of neutrino oscillations and
therefore of non-zero neutrino mass. These data imply a lower limit
on the hot dark matter (i.e., light neutrino) contribution to the
cosmological density
0.001.
is
actually that low, and therefore cosmologically uninteresting, if
m(
) >>
m(µ), as is
suggested by the hierarchical
pattern of the quark and charged lepton masses. But if the
and µ are nearly
degenerate in mass, as suggested by their strong mixing, then
could be substantially larger.
Although the Cold + Hot Dark Matter (CHDM) cosmological model with
h 
0.5,
m = 1, and
= 0.2 predicts power
spectra of cosmic density and CMB anisotropies that are in excellent
agreement with the data
(Primack 1997,
Gawiser & Silk 1998),
as we have just seen the large value measured for the Hubble parameter makes
such m = 1 models
dubious. It remains to be seen whether
including a significant amount of hot dark matter in
low-m
models improves their agreement with data.
Primack & Gross (1998)
found that the possible improvement of the
low-m flat
(
CDM)
cosmological models with the addition of light neutrinos appears to be
rather limited, and the maximum amount of hot dark matter decreases
with decreasing m
(Primack et al. 1995).
For m
0.4,
Croft, Hu, and Davé
(1999)
find that
0.08.
Fukugita et al. (1999)
find more restrictive upper limits with
the constraint that the primordial power spectrum index n
1, but
this may not be well motivated.